A time-reversal division multiple access (TRDMA) system provides a cost-effective single-carrier technology for broadband communications and at the same time leverages the degrees of freedom in a large number of multi-paths to form a unique high-resolution spatial focusing effect. In some time-reversal communication systems, when a transceiver A intends to transmit information to a transceiver B, transceiver B first sends a delta-like pilot pulse that propagates through a scattering and multi-path environment, and the signals are received by transceiver A. Transceiver A transmits time-reversed signals back through the same channel to transceiver B. Based on channel reciprocity, a time-reversal communication system leverages the multi-path channel as a matched filter, i.e., treats the environment as a facilitating matched filter computing machine, and focuses the wave at the receiver in both space and time domains. When the symbol rate is very high, inter-symbol interference (ISI) may occur and reduce the performance of the system.